Notes of booelan algebra

1. 2.2 PERFORM OPERATON
WITH BOOLEAN
ALGEBRA

2. LEARNING OUTCOME
1. Define logic gate
2. Explain the operation of logic gate
3. Draw the logic symbol for the following logic gate: NOT, AND,
OR, NAND, EX-OR, EX-NOR
4. Develop truth table

3. EXAMPLE OF IC : AND, OR, NOT
GATE
IC 7408 – AND gate IC 7404 – NOT gate IC 7432 – OR gate

6. INTRODUCTION
• Logic gates are the basic building blocks for forming digital
electronic circuitry.
• A logic gate has one output terminal and one or more input
terminals.
• Its output will be HIGH (1) or LOW (0) depending on the digital
level(s) at the input terminal(s).

7. • Through the use of logic gates, we can design digital systems
that will evaluate digital input levels and produce a specific output
response based on that particular logic circuit design.
• The five basic logic gates are the NOT (inverter), AND, OR,
NAND, NOR.ex or, ex nor

8. THE AND GATE
• The output, X is HIGH if input A and input B are both HIGH. In
other words, if A = 1 and B = 1, then X = 1.
• If either A or B or both are LOW, the output will be LOW.
A
B
Y
Y = A . B
Input A Input B Output Y
0 0 0
0 1 0
1 0 0
1 1 1

9. 7408 Quad 2-input AND Gate

10. THE OR GATE
• The OR gate also has two or more inputs and a single output.
• The operation of the two-input OR gate is defined as follows: The
output at Y will be HIGH whenever input A or input B is HIGH
or both are HIGH.
A
B Y
Y = A + B
Input A Input B Output Y
0 0 0
0 1 1
1 0 1
1 1 1

11. 7432 Quad 2-input Logic OR Gate

12. THE NOT GATE (INVERTER)
• The inverter is used to complement, or invert the digital signal.
• It has a single input and a single output.
• If a HIGH level (1) comes in, it produces a LOW-level (0)
output. If a LOW level (0) comes in, it produces a HIGH-level
(1) output.

13. THE NOT GATE (INVERTER)
Input A Output Y
0 1
1 0
A Y
AY 
Truth table:
Symbol:
Equation:

14. 7404 NOT Gate or Inverter

15. THE NAND GATE
• The operation of the NAND gate is the same as the AND gate
except that its output is inverted.
• You can think of a NAND gate as an AND gate with in inverter at
is output.
• The symbol for a NAND gate is made from an AND gate with the
inversion circle (bubble) at its output.

16. Y = AB
A
B
Y = AB = NOT ( A AND B )
A
Input Output
A B Y
0 0 1
0 1 1
1 0 1
1 1 0
Symbol & Truth table of the NAND gate

17. 7400 Quad 2-input Logic NAND Gate

18. THE NOR GATE
• The operation of the NOR gate is the same as the OR gate
except that its output is inverted.
• You can think of a NOR gate as an OR gate with in inverter at is
output.
• The symbol for a NOR gate is made from an OR gate with the
inversion circle (bubble) at its output.

19. SYMBOL & TRUTH TABLE OF
THE NOR GATE
Input Output
A B Y
0 0 1
0 1 0
1 0 0
1 1 0

20. 7402 Quad 2-input NOR Gate

21. THE EXCLUSIVE-OR GATE
• Provides a HIGH output if one input or the other input is
HIGH, but not both.
• The Boolean equation for the Ex-OR function is written X=AB +
AB and can be constructed using the combinational logic.

22. SYMBOL AND TRUTH TABLE OF THE
EXCLUSIVE-OR GATE
Input Output
A B EX – OR
0 0 0
0 1 1
1 0 1
1 1 0
• No of input 1 is even output 0
• No of input 1 is odd output 1

24. 7486 Quad 2-input Exclusive-OR Gate

25. THE EXCLUSIVE-NOR GATE
• The Exclusive-NOR is the complement of the exclusive-OR.
• The truth table for the Ex-NOR shows a HIGH output for both
inputs LOW and both inputs HIGH.
• The Ex-NOR is sometimes called the equality gate because both
inputs must be equal to get a HIGH output.

26. SYMBOL AND TRUTH TABLE OF THE
EXCLUSIVE-NOR GATE

27. EQUIVALENT CIRCUIT

28. EXERCISE
• 1) Develop truth table for 3 input Exclusive-OR gate
• 2) Develop truth table for 3 input Exclusive-NOR gate